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<div class="header">
  <div class="summary">
<a href="classEigen_1_1ComplexSchur-members.html">List of all members</a> &#124;
<a href="#pub-types">Public Types</a> &#124;
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pub-static-attribs">Static Public Attributes</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::ComplexSchur&lt; MatrixType_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__Eigenvalues__Module.html">Eigenvalues module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_&gt;<br />
class Eigen::ComplexSchur&lt; MatrixType_ &gt;</h3>

<p>Performs a complex Schur decomposition of a real or complex square matrix. </p>
<p>This is defined in the Eigenvalues module.</p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/Eigenvalues&gt;</span> </div>
</div><!-- fragment --><dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which we are computing the Schur decomposition; this is expected to be an instantiation of the <a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors.">Matrix</a> class template.</td></tr>
  </table>
  </dd>
</dl>
<p>Given a real or complex square matrix A, this class computes the Schur decomposition: \( A = U T U^*\) where U is a unitary complex matrix, and T is a complex upper triangular matrix. The diagonal of the matrix T corresponds to the eigenvalues of the matrix A.</p>
<p>Call the function <a class="el" href="classEigen_1_1ComplexSchur.html#ae4168c4ec8e7f7a5dbf4ea375769da12" title="Computes Schur decomposition of given matrix.">compute()</a> to compute the Schur decomposition of a given matrix. Alternatively, you can use the ComplexSchur(const MatrixType&amp;, bool) constructor which computes the Schur decomposition at construction time. Once the decomposition is computed, you can use the <a class="el" href="classEigen_1_1ComplexSchur.html#a303ad2c7a9dec4d809e4fe99dc3546d4" title="Returns the unitary matrix in the Schur decomposition.">matrixU()</a> and <a class="el" href="classEigen_1_1ComplexSchur.html#a37c059ee46b559129726693f7a0878d0" title="Returns the triangular matrix in the Schur decomposition.">matrixT()</a> functions to retrieve the matrices U and V in the decomposition.</p>
<dl class="section note"><dt>Note</dt><dd>This code is inspired from Jampack</dd></dl>
<dl class="section see"><dt>See also</dt><dd>class <a class="el" href="classEigen_1_1RealSchur.html" title="Performs a real Schur decomposition of a square matrix.">RealSchur</a>, class <a class="el" href="classEigen_1_1EigenSolver.html" title="Computes eigenvalues and eigenvectors of general matrices.">EigenSolver</a>, class <a class="el" href="classEigen_1_1ComplexEigenSolver.html" title="Computes eigenvalues and eigenvectors of general complex matrices.">ComplexEigenSolver</a> </dd></dl>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:abed305877f8fec28d44a4e46fec72cb6"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt; <a class="el" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a>, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6">ComplexMatrixType</a></td></tr>
<tr class="memdesc:abed305877f8fec28d44a4e46fec72cb6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Type for the matrices in the Schur decomposition.  <a href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6">More...</a><br /></td></tr>
<tr class="separator:abed305877f8fec28d44a4e46fec72cb6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9cfc7d20234dd51933b0cb6ef427c8b4"><td class="memItemLeft" align="right" valign="top">typedef std::complex&lt; RealScalar &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a></td></tr>
<tr class="memdesc:a9cfc7d20234dd51933b0cb6ef427c8b4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Complex scalar type for <code>MatrixType_</code>.  <a href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">More...</a><br /></td></tr>
<tr class="separator:a9cfc7d20234dd51933b0cb6ef427c8b4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8e273074f2cafe49725fcc774b93d6bf"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a></td></tr>
<tr class="separator:a8e273074f2cafe49725fcc774b93d6bf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3121a90f56446ec9a68f53f9b79bef9c"><td class="memItemLeft" align="right" valign="top"><a id="a3121a90f56446ec9a68f53f9b79bef9c"></a>
typedef MatrixType::Scalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a3121a90f56446ec9a68f53f9b79bef9c">Scalar</a></td></tr>
<tr class="memdesc:a3121a90f56446ec9a68f53f9b79bef9c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Scalar type for matrices of type <code>MatrixType_</code>. <br /></td></tr>
<tr class="separator:a3121a90f56446ec9a68f53f9b79bef9c"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:ab5745362c6c27d259188a06b7ba74733"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:ab5745362c6c27d259188a06b7ba74733"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#ab5745362c6c27d259188a06b7ba74733">ComplexSchur</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix, bool computeU=true)</td></tr>
<tr class="memdesc:ab5745362c6c27d259188a06b7ba74733"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor; computes Schur decomposition of given matrix.  <a href="classEigen_1_1ComplexSchur.html#ab5745362c6c27d259188a06b7ba74733">More...</a><br /></td></tr>
<tr class="separator:ab5745362c6c27d259188a06b7ba74733"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a49e78b336c89147fdc80589444884b1b"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a49e78b336c89147fdc80589444884b1b">ComplexSchur</a> (<a class="el" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> size=RowsAtCompileTime==<a class="el" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? 1 :RowsAtCompileTime)</td></tr>
<tr class="memdesc:a49e78b336c89147fdc80589444884b1b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default constructor.  <a href="classEigen_1_1ComplexSchur.html#a49e78b336c89147fdc80589444884b1b">More...</a><br /></td></tr>
<tr class="separator:a49e78b336c89147fdc80589444884b1b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae4168c4ec8e7f7a5dbf4ea375769da12"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:ae4168c4ec8e7f7a5dbf4ea375769da12"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#ae4168c4ec8e7f7a5dbf4ea375769da12">compute</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix, bool computeU=true)</td></tr>
<tr class="memdesc:ae4168c4ec8e7f7a5dbf4ea375769da12"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes Schur decomposition of given matrix.  <a href="classEigen_1_1ComplexSchur.html#ae4168c4ec8e7f7a5dbf4ea375769da12">More...</a><br /></td></tr>
<tr class="separator:ae4168c4ec8e7f7a5dbf4ea375769da12"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa1fd35f3ae0ccbdecb9e200dcad14324"><td class="memTemplParams" colspan="2">template&lt;typename HessMatrixType , typename OrthMatrixType &gt; </td></tr>
<tr class="memitem:aa1fd35f3ae0ccbdecb9e200dcad14324"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#aa1fd35f3ae0ccbdecb9e200dcad14324">computeFromHessenberg</a> (const HessMatrixType &amp;matrixH, const OrthMatrixType &amp;matrixQ, bool computeU=true)</td></tr>
<tr class="memdesc:aa1fd35f3ae0ccbdecb9e200dcad14324"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute Schur decomposition from a given Hessenberg matrix.  <a href="classEigen_1_1ComplexSchur.html#aa1fd35f3ae0ccbdecb9e200dcad14324">More...</a><br /></td></tr>
<tr class="separator:aa1fd35f3ae0ccbdecb9e200dcad14324"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6f35999b87c247bb24b2ad6ba1abee69"><td class="memItemLeft" align="right" valign="top"><a id="a6f35999b87c247bb24b2ad6ba1abee69"></a>
<a class="el" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a6f35999b87c247bb24b2ad6ba1abee69">getMaxIterations</a> ()</td></tr>
<tr class="memdesc:a6f35999b87c247bb24b2ad6ba1abee69"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the maximum number of iterations. <br /></td></tr>
<tr class="separator:a6f35999b87c247bb24b2ad6ba1abee69"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a13adef2a54e61bb5789eb7821a3b7b46"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a13adef2a54e61bb5789eb7821a3b7b46">info</a> () const</td></tr>
<tr class="memdesc:a13adef2a54e61bb5789eb7821a3b7b46"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reports whether previous computation was successful.  <a href="classEigen_1_1ComplexSchur.html#a13adef2a54e61bb5789eb7821a3b7b46">More...</a><br /></td></tr>
<tr class="separator:a13adef2a54e61bb5789eb7821a3b7b46"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a37c059ee46b559129726693f7a0878d0"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6">ComplexMatrixType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a37c059ee46b559129726693f7a0878d0">matrixT</a> () const</td></tr>
<tr class="memdesc:a37c059ee46b559129726693f7a0878d0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the triangular matrix in the Schur decomposition.  <a href="classEigen_1_1ComplexSchur.html#a37c059ee46b559129726693f7a0878d0">More...</a><br /></td></tr>
<tr class="separator:a37c059ee46b559129726693f7a0878d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a303ad2c7a9dec4d809e4fe99dc3546d4"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6">ComplexMatrixType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a303ad2c7a9dec4d809e4fe99dc3546d4">matrixU</a> () const</td></tr>
<tr class="memdesc:a303ad2c7a9dec4d809e4fe99dc3546d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the unitary matrix in the Schur decomposition.  <a href="classEigen_1_1ComplexSchur.html#a303ad2c7a9dec4d809e4fe99dc3546d4">More...</a><br /></td></tr>
<tr class="separator:a303ad2c7a9dec4d809e4fe99dc3546d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab559c4b9a0a742091c4b15b84a6ddf97"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#ab559c4b9a0a742091c4b15b84a6ddf97">setMaxIterations</a> (<a class="el" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> maxIters)</td></tr>
<tr class="memdesc:ab559c4b9a0a742091c4b15b84a6ddf97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sets the maximum number of iterations allowed.  <a href="classEigen_1_1ComplexSchur.html#ab559c4b9a0a742091c4b15b84a6ddf97">More...</a><br /></td></tr>
<tr class="separator:ab559c4b9a0a742091c4b15b84a6ddf97"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-attribs"></a>
Static Public Attributes</h2></td></tr>
<tr class="memitem:a79450087274edce80ee268e2f42e64f1"><td class="memItemLeft" align="right" valign="top">static const int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ComplexSchur.html#a79450087274edce80ee268e2f42e64f1">m_maxIterationsPerRow</a></td></tr>
<tr class="memdesc:a79450087274edce80ee268e2f42e64f1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum number of iterations per row.  <a href="classEigen_1_1ComplexSchur.html#a79450087274edce80ee268e2f42e64f1">More...</a><br /></td></tr>
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<h2 class="groupheader">Member Typedef Documentation</h2>
<a id="abed305877f8fec28d44a4e46fec72cb6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abed305877f8fec28d44a4e46fec72cb6">&#9670;&nbsp;</a></span>ComplexMatrixType</h2>

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template&lt;typename MatrixType_ &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt;<a class="el" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a>, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime&gt; <a class="el" href="classEigen_1_1ComplexSchur.html">Eigen::ComplexSchur</a>&lt; MatrixType_ &gt;::<a class="el" href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6">ComplexMatrixType</a></td>
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<p>Type for the matrices in the Schur decomposition. </p>
<p>This is a square matrix with entries of type <a class="el" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4" title="Complex scalar type for MatrixType_.">ComplexScalar</a>. The size is the same as the size of <code>MatrixType_</code>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a9cfc7d20234dd51933b0cb6ef427c8b4">&#9670;&nbsp;</a></span>ComplexScalar</h2>

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template&lt;typename MatrixType_ &gt; </div>
      <table class="memname">
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          <td class="memname">typedef std::complex&lt;RealScalar&gt; <a class="el" href="classEigen_1_1ComplexSchur.html">Eigen::ComplexSchur</a>&lt; MatrixType_ &gt;::<a class="el" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a></td>
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<p>Complex scalar type for <code>MatrixType_</code>. </p>
<p>This is <code>std::complex&lt;Scalar&gt;</code> if <a class="el" href="classEigen_1_1ComplexSchur.html#a3121a90f56446ec9a68f53f9b79bef9c" title="Scalar type for matrices of type MatrixType_.">Scalar</a> is real (e.g., <code>float</code> or <code>double</code>) and just <code>Scalar</code> if <a class="el" href="classEigen_1_1ComplexSchur.html#a3121a90f56446ec9a68f53f9b79bef9c" title="Scalar type for matrices of type MatrixType_.">Scalar</a> is complex. </p>

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<dl class="deprecated"><dt><b><a class="el" href="deprecated.html#_deprecated000013">Deprecated:</a></b></dt><dd>since <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> 3.3 </dd></dl>

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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a49e78b336c89147fdc80589444884b1b">&#9670;&nbsp;</a></span>ComplexSchur() <span class="overload">[1/2]</span></h2>

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          <td class="memname"><a class="el" href="classEigen_1_1ComplexSchur.html">Eigen::ComplexSchur</a>&lt; MatrixType_ &gt;::<a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a> </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a>&#160;</td>
          <td class="paramname"><em>size</em> = <code>RowsAtCompileTime==<a class="el" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>&#160;?&#160;1&#160;:&#160;RowsAtCompileTime</code></td><td>)</td>
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<p>Default constructor. </p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramdir">[in]</td><td class="paramname">size</td><td>Positive integer, size of the matrix whose Schur decomposition will be computed.</td></tr>
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<p>The default constructor is useful in cases in which the user intends to perform decompositions via <a class="el" href="classEigen_1_1ComplexSchur.html#ae4168c4ec8e7f7a5dbf4ea375769da12" title="Computes Schur decomposition of given matrix.">compute()</a>. The <code>size</code> parameter is only used as a hint. It is not an error to give a wrong <code>size</code>, but it may impair performance.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1ComplexSchur.html#ae4168c4ec8e7f7a5dbf4ea375769da12" title="Computes Schur decomposition of given matrix.">compute()</a> for an example. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ab5745362c6c27d259188a06b7ba74733">&#9670;&nbsp;</a></span>ComplexSchur() <span class="overload">[2/2]</span></h2>

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          <td>(</td>
          <td class="paramtype">const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
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<p>Constructor; computes Schur decomposition of given matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose Schur decomposition is to be computed. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">computeU</td><td>If true, both T and U are computed; if false, only T is computed.</td></tr>
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<p>This constructor calls <a class="el" href="classEigen_1_1ComplexSchur.html#ae4168c4ec8e7f7a5dbf4ea375769da12" title="Computes Schur decomposition of given matrix.">compute()</a> to compute the Schur decomposition.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1ComplexSchur.html#a37c059ee46b559129726693f7a0878d0" title="Returns the triangular matrix in the Schur decomposition.">matrixT()</a> and <a class="el" href="classEigen_1_1ComplexSchur.html#a303ad2c7a9dec4d809e4fe99dc3546d4" title="Returns the unitary matrix in the Schur decomposition.">matrixU()</a> for examples. </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae4168c4ec8e7f7a5dbf4ea375769da12">&#9670;&nbsp;</a></span>compute()</h2>

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          <td class="memname"><a class="el" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>&amp; <a class="el" href="classEigen_1_1ComplexSchur.html">Eigen::ComplexSchur</a>&lt; MatrixType_ &gt;::compute </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
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<p>Computes Schur decomposition of given matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose Schur decomposition is to be computed. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">computeU</td><td>If true, both T and U are computed; if false, only T is computed.</td></tr>
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<dl class="section return"><dt>Returns</dt><dd>Reference to <code>*this</code> </dd></dl>
<p>The Schur decomposition is computed by first reducing the matrix to Hessenberg form using the class <a class="el" href="classEigen_1_1HessenbergDecomposition.html" title="Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.">HessenbergDecomposition</a>. The Hessenberg matrix is then reduced to triangular form by performing QR iterations with a single shift. The cost of computing the Schur decomposition depends on the number of iterations; as a rough guide, it may be taken on the number of iterations; as a rough guide, it may be taken to be \(25n^3\) complex flops, or \(10n^3\) complex flops if <em>computeU</em> is false.</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#gae40207c482eaada1403778d301236443">MatrixXcf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXcf::Random</a>(4,4);</div>
<div class="line">ComplexSchur&lt;MatrixXcf&gt; schur(4);</div>
<div class="line">schur.compute(A);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The matrix T in the decomposition of A is:&quot;</span> &lt;&lt; endl &lt;&lt; schur.matrixT() &lt;&lt; endl;</div>
<div class="line">schur.compute(A.inverse());</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The matrix T in the decomposition of A^(-1) is:&quot;</span> &lt;&lt; endl &lt;&lt; schur.matrixT() &lt;&lt; endl;</div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_ae814abb451b48ed872819192dc188c19"><div class="ttname"><a href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Eigen::DenseBase::Random</a></div><div class="ttdeci">static const RandomReturnType Random()</div><div class="ttdef"><b>Definition:</b> Random.h:114</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_gae40207c482eaada1403778d301236443"><div class="ttname"><a href="group__matrixtypedefs.html#gae40207c482eaada1403778d301236443">Eigen::MatrixXcf</a></div><div class="ttdeci">Matrix&lt; std::complex&lt; float &gt;, Dynamic, Dynamic &gt; MatrixXcf</div><div class="ttdoc">Dynamic×Dynamic matrix of type std::complex&lt;float&gt;.</div><div class="ttdef"><b>Definition:</b> Matrix.h:502</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">The matrix T in the decomposition of A is:
 (-0.691,-1.63)  (0.763,-0.144) (-0.104,-0.836) (-0.462,-0.378)
          (0,0)   (-0.758,1.22)  (-0.65,-0.772)  (-0.244,0.113)
          (0,0)           (0,0)   (0.137,0.505) (0.0687,-0.404)
          (0,0)           (0,0)           (0,0)   (1.52,-0.402)
The matrix T in the decomposition of A^(-1) is:
    (0.501,-1.84)    (-1.01,-0.984)       (0.636,1.3)    (-0.676,0.352)
            (0,0)   (-0.369,-0.593)     (0.0733,0.18) (-0.0658,-0.0263)
            (0,0)             (0,0)    (-0.222,0.521)    (-0.191,0.121)
            (0,0)             (0,0)             (0,0)     (0.614,0.162)
</pre><dl class="section see"><dt>See also</dt><dd>compute(const MatrixType&amp;, bool, Index) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aa1fd35f3ae0ccbdecb9e200dcad14324">&#9670;&nbsp;</a></span>computeFromHessenberg()</h2>

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template&lt;typename HessMatrixType , typename OrthMatrixType &gt; </div>
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<p>Compute Schur decomposition from a given Hessenberg matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">matrixH</td><td><a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors.">Matrix</a> in Hessenberg form H </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">matrixQ</td><td>orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T </td></tr>
    <tr><td class="paramdir"></td><td class="paramname">computeU</td><td>Computes the matriX U of the Schur vectors </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>Reference to <code>*this</code> </dd></dl>
<p>This routine assumes that the matrix is already reduced in Hessenberg form matrixH using either the class <a class="el" href="classEigen_1_1HessenbergDecomposition.html" title="Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.">HessenbergDecomposition</a> or another mean. It computes the upper quasi-triangular matrix T of the Schur decomposition of H When computeU is true, this routine computes the matrix U such that A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix</p>
<p>NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix is not available, the user should give an identity matrix (Q.setIdentity())</p>
<dl class="section see"><dt>See also</dt><dd>compute(const MatrixType&amp;, bool) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a13adef2a54e61bb5789eb7821a3b7b46">&#9670;&nbsp;</a></span>info()</h2>

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<p>Reports whether previous computation was successful. </p>
<dl class="section return"><dt>Returns</dt><dd><code>Success</code> if computation was successful, <code>NoConvergence</code> otherwise. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a37c059ee46b559129726693f7a0878d0">&#9670;&nbsp;</a></span>matrixT()</h2>

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<p>Returns the triangular matrix in the Schur decomposition. </p>
<dl class="section return"><dt>Returns</dt><dd>A const reference to the matrix T.</dd></dl>
<p>It is assumed that either the constructor ComplexSchur(const MatrixType&amp; matrix, bool computeU) or the member function compute(const MatrixType&amp; matrix, bool computeU) has been called before to compute the Schur decomposition of a matrix.</p>
<p>Note that this function returns a plain square matrix. If you want to reference only the upper triangular part, use: </p><div class="fragment"><div class="line">schur.matrixT().triangularView&lt;<a class="code" href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Upper</a>&gt;() </div>
<div class="ttc" id="agroup__enums_html_gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1"><div class="ttname"><a href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Eigen::Upper</a></div><div class="ttdeci">@ Upper</div><div class="ttdef"><b>Definition:</b> Constants.h:213</div></div>
</div><!-- fragment --><p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#gae40207c482eaada1403778d301236443">MatrixXcf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXcf::Random</a>(4,4);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is a random 4x4 matrix, A:&quot;</span> &lt;&lt; endl &lt;&lt; A &lt;&lt; endl &lt;&lt; endl;</div>
<div class="line">ComplexSchur&lt;MatrixXcf&gt; schurOfA(A, <span class="keyword">false</span>); <span class="comment">// false means do not compute U</span></div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The triangular matrix T is:&quot;</span> &lt;&lt; endl &lt;&lt; schurOfA.matrixT() &lt;&lt; endl;</div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is a random 4x4 matrix, A:
  (-0.211,0.68)  (0.108,-0.444)   (0.435,0.271) (-0.198,-0.687)
  (0.597,0.566) (0.258,-0.0452)  (0.214,-0.717)  (-0.782,-0.74)
 (-0.605,0.823)  (0.0268,-0.27) (-0.514,-0.967)  (-0.563,0.998)
  (0.536,-0.33)   (0.832,0.904)  (0.608,-0.726)  (0.678,0.0259)

The triangular matrix T is:
 (-0.691,-1.63)  (0.763,-0.144) (-0.104,-0.836) (-0.462,-0.378)
          (0,0)   (-0.758,1.22)  (-0.65,-0.772)  (-0.244,0.113)
          (0,0)           (0,0)   (0.137,0.505) (0.0687,-0.404)
          (0,0)           (0,0)           (0,0)   (1.52,-0.402)
</pre> 
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<h2 class="memtitle"><span class="permalink"><a href="#a303ad2c7a9dec4d809e4fe99dc3546d4">&#9670;&nbsp;</a></span>matrixU()</h2>

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<p>Returns the unitary matrix in the Schur decomposition. </p>
<dl class="section return"><dt>Returns</dt><dd>A const reference to the matrix U.</dd></dl>
<p>It is assumed that either the constructor ComplexSchur(const MatrixType&amp; matrix, bool computeU) or the member function compute(const MatrixType&amp; matrix, bool computeU) has been called before to compute the Schur decomposition of a matrix, and that <code>computeU</code> was set to true (the default value).</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#gae40207c482eaada1403778d301236443">MatrixXcf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXcf::Random</a>(4,4);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is a random 4x4 matrix, A:&quot;</span> &lt;&lt; endl &lt;&lt; A &lt;&lt; endl &lt;&lt; endl;</div>
<div class="line">ComplexSchur&lt;MatrixXcf&gt; schurOfA(A);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The unitary matrix U is:&quot;</span> &lt;&lt; endl &lt;&lt; schurOfA.matrixU() &lt;&lt; endl;</div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is a random 4x4 matrix, A:
  (-0.211,0.68)  (0.108,-0.444)   (0.435,0.271) (-0.198,-0.687)
  (0.597,0.566) (0.258,-0.0452)  (0.214,-0.717)  (-0.782,-0.74)
 (-0.605,0.823)  (0.0268,-0.27) (-0.514,-0.967)  (-0.563,0.998)
  (0.536,-0.33)   (0.832,0.904)  (0.608,-0.726)  (0.678,0.0259)

The unitary matrix U is:
 (-0.122,0.271)   (0.354,0.255)    (-0.7,0.321) (0.0909,-0.346)
   (0.247,0.23)  (0.435,-0.395)   (0.184,-0.38)  (0.492,-0.347)
(0.859,-0.0877)  (0.00469,0.21) (-0.256,0.0163)   (0.133,0.355)
 (-0.116,0.195) (-0.484,-0.432)  (-0.183,0.359)   (0.559,0.231)
</pre> 
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<h2 class="memtitle"><span class="permalink"><a href="#ab559c4b9a0a742091c4b15b84a6ddf97">&#9670;&nbsp;</a></span>setMaxIterations()</h2>

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<p>Sets the maximum number of iterations allowed. </p>
<p>If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size of the matrix. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a79450087274edce80ee268e2f42e64f1">&#9670;&nbsp;</a></span>m_maxIterationsPerRow</h2>

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<p>Maximum number of iterations per row. </p>
<p>If not otherwise specified, the maximum number of iterations is this number times the size of the matrix. It is currently set to 30. </p>

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